Assignment #5 - site.uottawa.casloyka/elg3175/A5_3175.pdf · Assignment #5 Due: Mar. 13, 8:30am,...
Transcript of Assignment #5 - site.uottawa.casloyka/elg3175/A5_3175.pdf · Assignment #5 Due: Mar. 13, 8:30am,...
x
( )( ) ( ) cosc c
x t A m t t= ω
3rd
power
device
BPF
f0=3fc
Ideal
limiter
BPF
f0=3fc
Frequency divider
3÷
LPF
1( )x t
2( )x t 3( )x t 4( )x t5( )x t
6( )x t ( )y t
frequency multiplier
x2
frequency multiplier
x5
In Out
ELG3175: Introduction to Communication Systems, Winter 2018, © S. Loyka
Assignment #5
Due: Mar. 13, 8:30am, SMD 425 (the tutorial). Hard copy only, no email submissions. Late entries will not be
accepted!
1) An inexperienced engineer has designed the following DSB-SC demodulator:
a) Find x1(t)- x6(t) and y(t). Is it a demodulator? Why? b) Consider a
special case of ( ) sin ,c
m t t= Ω Ω << ω
and sketch m(t) and y(t) on the same graph. Are they the same? Assume
that the amplitude of y(t) is 1. Note:
3rd power device has the following
input-output characteristic: 3( ) ( )
out inx t x t= . Ideal limiter input-output characteristic is ( )( ) sgn ( )
out inx t x t= .
2) The normalized signal ( )n
m t has a bandwidth of 10 kHz and its power is 0.4 W. The carrier 0
cos 2A f tπ has a
power of 100 W. (a) If ( )n
m t modulates the carrier using DSB-SC amplitude modulation, what will be the bandwidth
and the power content of the modulated signal? (b) If the modulation scheme is conventional AM with modulation
index of 0.8, what will be the answer to part a? (c) If modulation is FM with with 35 10fk = ⋅ , what will be the answer
to part a?
3) An angle modulated signal has the form ( ) 20cos[2 4sin 2000 ]c
u t f t t= π + π where 10cf MHz= . (a) Determine the
average transmitted power. (b) Determine the peak-phase deviation. (c) Determine the peak-frequency deviation. (d) Is
this an FM or a PM signal? Explain.
4) The carrier 6( ) cos2 10c t A t= π is angle modulated (PM or FM) by the sinusoid signal ( ) 2cos2000m t t= π . The
deviation constants are 1.5 /p
k rad V= and 3000 /fk Hz V= . (a) Determine fβ and pβ . (b) Determine the bandwidth in
each case using Carson’s rule. (c) Plot the spectrum of the modulated signal in each case (plot only those frequency
components that lie within the bandwidth derived in part b.) (d) If the amplitude of ( )m t is decreased by a factor of two,
how would your answers to part a-c change? (e) If the frequency of ( )m t is increased by a factor of two, how would
your answers to part a-c change?
5) Consider the following wideband FM modulator. Assume that there
are appropriate bandpass filters in the 1st and 2nd multipliers. The input to the
modulator is a narrowband FM signal with the peak frequency deviation
2 kHzf∆ = and the message is 4( ) 5sin(10 )m t t= π . (a) Find the frequency
separation of the components in the FM signal spectrum at the output of the 1st multiplier. (b) Find the peak frequency deviation at the output of the 1st multiplier. (c) Repeat (a) and (b) for the output of the 2nd multiplier and find the
bandwidth of the output wideband FM signal.
_______________________________________________________________________________________________ * Please give detailed solutions, not just final answers. Do not skip important steps.
* Plagiarism (i.e. “cut-and-paste” from a student to a student, other forms of “borrowing” the material for the assignment) is
absolutely unacceptable and will be penalized. Each student is expected to submit his own solutions. If two (or more) identical or almost identical sets of solutions are found, each student involved receives 0 (zero) for that particular assignment. If this happens
twice, the students involved receive 0 (zero) for the entire assignment component of the course in the marking scheme and the case
will be send to the Dean’s office for further investigation.